A dual-radar multi-target real-time tracking method considering system error correction

Abstract

The application discloses a kind of double radar multi-target real-time tracking method considering system error correction, it is related to radar target tracking field.The method includes: coordinate conversion and error conversion are carried out to radar data, and observation data set is formed;The observation of a radar is used to start track for multi-target, and continue to associate to filter error and keep stable;After correct and stable multi-target track has been formed, the observation data of another radar is added, and the measurement data encountered subsequently is translated by a certain distance to correct the deviation of measurement value due to the system deviation of two radars;Joint probability density data association is generated, the probability of each feasible event is calculated, and joint association probability is formed;Consider multiple nonlinear filter models, and the interactive multi-mode algorithm based on unscented Kalman filter is used for filtering.The application can make the association of plot and track in multi-target tracking problem more accurate by correcting the deviation, and better tracking effect is realized.

Description

Technical Field

[0001] This invention relates to target tracking technology in the field of radar, specifically a real-time dual-radar multi-target tracking method based on Joint Probabilistic Data Association (JPDA) and considering system error correction. Background Technology

[0002] For multi-target tracking in a dual-radar system, the measurements from both radars are typically converted to a unified coordinate system before subsequent correlation and filtering. However, radars not only have random errors but also systematic biases (including positional and angular deviations in three directions) caused by factors such as installation. These systematic biases can lead to slight deviations in the measurements of the same target from the two radars in the unified coordinate system. This deviation can cause incorrect correlations in situations involving multiple targets at close range (such as flight formations), resulting in poor tracking performance. Summary of the Invention

[0003] In view of this, the present invention provides a dual-radar multi-target real-time tracking method that takes into account system error correction, which can correct system deviations to a certain extent and achieve better tracking results.

[0004] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0005] A real-time multi-target tracking method using dual radars that considers system error correction includes the following steps:

[0006] Step 1: Configure the radar system parameters, including sensor ID, sensor data transmission period, sensor latitude and longitude, measurement error, and detection range. After the radar transmits the point traces, convert the distance, azimuth, and elevation measurements of the two radars A and B into a unified Cartesian coordinate system, and convert the radar measurement error into Cartesian coordinates to form an observation dataset in the Cartesian coordinate system. The measurements and measurement errors in the Cartesian coordinate system are used for joint probability distribution data association, while the measurements and measurement errors in the radar spherical coordinate system are used for filtering and updating.

[0007] Step 2: Use radar A's observations to initiate tracks for multiple targets. Use a logical method to initiate and terminate tracks. Assume that the sequence of observations contains N scan cycles. If the number of successful detections reaches the threshold M within a time window containing N scan cycles, then the track is successfully started. After the start is completed, continue to associate with the filtering error to maintain stability.

[0008] Step 3: After a correct and stable multi-target track has been formed, add the observation data from radar B. The first set of measurement data from radar B encountered subsequently is shifted to coincide with the center of the graphic formed by the extension points of all tracks. A correction window w is set, and the shift S of the nth set of measurement data from radar B encountered subsequently is:

[0009]

[0010] x n This represents the offset of the nth set of measurement data from radar B.

[0011] The measurement data of radar B is shifted according to the shift amount S, and the shifted measurement data is used as new measurement data in subsequent correlation and filtering.

[0012] Step 4: Based on whether all measurement data fall into the tracking gate of each track extension point, a confirmation matrix is ​​formed. The confirmation matrix is ​​then split into multiple feasible events using a depth search algorithm. The maximum likelihood probability of each feasible event is calculated using the posterior probability formula. The probabilities of each feasible event are combined to form a joint correlation probability.

[0013] Step 5: For each measurement data associated with each track, perform IMM-UKF filtering based on the joint association probability. The specific method is as follows:

[0014] The input conditions of each unscented Kalman filter are a mixture of the estimates from the filters at the previous time step;

[0015] For each unscented Kalman filter, given the re-initialized state and covariance matrix, filtering is performed after obtaining new measurements;

[0016] Calculate the model probability for each filter;

[0017] Calculate the overall estimate and overall estimate error covariance at the current time based on the state estimate and model probability of each filter;

[0018] The state estimate and covariance estimate of each IMM-UKF filter are combined to obtain the final filtering result of the track.

[0019] The beneficial effects of this invention are as follows:

[0020] 1. Due to system bias, the measurement values ​​of two radars for the same target in a unified coordinate system will deviate to a certain extent, although this deviation is similar within a small range. This invention can effectively correct this deviation. Simulation experiments show that after a certain period, the offset of the measurement data of radar B tends to stabilize.

[0021] 2. To improve the target filtering accuracy, this invention adopts an unscented Kalman filtering method based on IMM, which can further improve the tracking effect on nonlinear moving targets. Attached Figure Description

[0022] Figure 1 This is a flowchart of the method of the present invention.

[0023] Figures 2a-2c These are the simulation results of the method of this invention. Detailed Implementation

[0024] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0025] A real-time multi-target tracking method using dual radars, considering system error correction, is proposed. First, the radar data undergoes coordinate and error transformation to form an observation dataset. Then, observations from one radar are used to initiate multi-target tracks, which are continuously correlated until the filtering error stabilizes. After a correct and stable multi-target track is established, observation data from the other radar is added, shifting subsequent measurement data by a certain distance to correct deviations in measurement values ​​caused by the system bias between the two radars. Next, joint probability density data correlation is performed to form a confirmation matrix, generating feasible events and calculating the probability of each feasible event to form a joint correlation probability. Finally, filtering is updated, considering multiple nonlinear filter models and employing an interactive multimode algorithm based on unscented Kalman filtering for filtering.

[0026] Specifically, such as Figure 1 As shown, the method includes the following steps:

[0027] Step 1 involves parameter setting and data preprocessing. System parameters include sensor ID, sensor data transmission cycle, sensor latitude and longitude, measurement error, and detection range. After the radar transmits its data points, the measurements (range, azimuth, and elevation) from both radars need to be converted to a unified Cartesian coordinate system (defaulting to the ideal coordinate system of the radar with the higher data rate, assumed to be radar A). The radar measurement error is also converted to Cartesian coordinates, forming an observation dataset in the Cartesian coordinate system. The measurements and measurement errors in the Cartesian coordinate system are used for joint probability distribution data association, while the measurements and measurement errors in the radar spherical coordinate system are used for filtering and updating.

[0028] Step 2, Track Formation: Tracks are initiated for multiple targets using observations from one of the radars (Radar A). A logical method is employed for track initiation and termination. Assuming the sequence of observations contains N scan cycles, if the number of successful detections reaches a threshold M within a time window containing N scan cycles, the track is successfully initiated. After initiation, correlation continues until the filtering error remains stable.

[0029] Step 3, Deviation Correction: After a correct and stable multi-target track has been formed, observation data from another radar (Radar B) is added. The first set of measurement data from Radar B encountered subsequently is shifted to coincide with the center of the graphic formed by the extension points of all tracks. A correction window w is set. The shift amount of the 2nd to wth sets of measurement data from Radar B is the average of the current offset and the sum of historical offsets. For example, the shift amount of the kth set of measurement data is the average of the offsets from the 1st to the kth sets, where 2≤k≤w. The shift amount of the (w+1)th set of measurement data from Radar B onwards is the weighted average of the current offset and the previous offset. Finally, the shifted measurement data is used as new measurement data in subsequent correlation and filtering.

[0030] Step 4: Joint probability density data association. A confirmation matrix is ​​formed by determining whether all measurement data fall into the tracking gate of each track extension point. The confirmation matrix is ​​then split into multiple feasible events using a depth search algorithm. The maximum likelihood probability of each feasible event is calculated using the posterior probability formula. The probabilities of each feasible event are combined to form a joint association probability.

[0031] Step 5, Filter Update: For each measurement data associated with each track, IMM-UKF filtering is performed according to the joint association probability mentioned above. This mainly includes four steps: Input Interaction: The input conditions of each unscented Kalman filter are formed by mixing the estimates of each filter at the previous time step; Model Condition Filtering: For each unscented Kalman filter, given the re-initialized state and covariance matrix, filtering is performed after obtaining new measurements; Model Probability Update: The model probability of each filter is calculated; Estimation Fusion: The overall estimate and overall estimate error covariance at the current time step are calculated based on the state estimate and model probability of each filter. Finally, the state estimate and covariance estimate of each IMM-UKF filter are combined to obtain the final filtering result for the track.

[0032] The method of the present invention is verified by simulation below. The specific steps are as follows:

[0033] Step 1, Parameter Settings and Story Simulation:

[0034] Simulation initial conditions: Three targets, two radars with scan cycles of 1s and 2.253s respectively; radar latitude, longitude, and altitude of (28.4, 119.2, 100) and (28.9, 119.9, 100) respectively; radar installation angle errors of (0.1°, 0.2°, -0.1°) and (0.2°, 0.2°, -0.1°) respectively; installation distance errors of (10m, 5m, 5m) and (-10m, 5m, -5m) meters respectively; random errors of range, azimuth, and elevation of (10m, 0.1°, 0.15°) and (5m, 0.1°, 0.1°) respectively. Assume no missed detections or false alarms by the radars. Assuming that the three targets are moving in uniform linear motion in formation, their initial states in the ideal coordinate system of radar A are [2500050-500050050], [2480050-480050050], and [2480050-520050050].

[0035] Step 2: Use the observations of one of the radars (radar 1) to initiate the trajectory of multiple targets and continue to correlate until the filtering error remains stable.

[0036] Step 3, Deviation Correction:

[0037] After a correct and stable multi-target track has been established, observation data from another radar (radar 2) is added. The first set of measurement data from radar 2 encountered subsequently is shifted to coincide with the center of the graphic formed by the extension points of the three tracks. The correction window is set to w = 5. The final shift S of each set of measurement data from radar 2 is shown in the following formula:

[0038]

[0039] Where, x n This represents the offset of the nth set of measurement data from radar 2.

[0040] The translated measurement data is used as new measurement data in subsequent correlation and filtering.

[0041] Step 4, Joint Probabilistic Data Association: The joint probabilistic data association method calculates the corresponding residuals for all points within a target association gate and weights these residuals to update the target trajectory. However, if a point is located in the overlapping area of ​​association gates for different targets, the competition for that point among multiple targets must be considered. To reflect the competition from other targets for that point, its corresponding weight should be reduced. Joint probabilistic data association consists of the following four steps:

[0042] (1) Forming a confirmation matrix

[0043]

[0044] In the formula, ω j,tIt is a binary variable, where ω j,t =1 indicates that the point j (j=1,…,m) k ) falls into the association gate of the target t (t=1,…,T), while ω j,t =0 indicates that point j does not fall within the association gate of target t. t=0 represents clutter, since every point may originate from clutter, therefore the values ​​of the first column elements of the Ω matrix are all set to 1. For a given point association problem, the confirmation matrix reflects the interconnection status between the point and the target or clutter.

[0045] (2) The confirmation matrix is ​​split to obtain multiple feasible matrices and the feasible events corresponding to each feasible matrix. Two principles must be followed when splitting the confirmation matrix: One and only one element with a value of 1 is selected from each row of the confirmation matrix; this element will be the unique non-zero element of the corresponding row in the association matrix. In the feasible matrix, each column except the first column can contain at most one non-zero element. The first principle indicates that each trace has a unique source, that is, the trace either originates from the target or from clutter; the second principle indicates that at each time step, each target generates at most one trace. The method for splitting the confirmation matrix is ​​usually a depth-first search algorithm.

[0046] (3) Calculate the maximum likelihood probability of each feasible event according to the posterior probability formula.

[0047] (4) The probability of association between each track and each measurement is calculated by combining the probabilities of each feasible event.

[0048] Step 5: Filtering is performed using the Interactive Multi-Model (IMM) algorithm, a suboptimal algorithm for state estimation of hybrid systems. At time k, when calculating the target state estimate using the IMM method, each model filter is considered to have the potential to become the currently effective system model filter. The initial conditions of each filter are a synthesis of the filtering results of the various models at the previous time step (synthetic initial conditions). The IMM model is generally considered one of the most effective hybrid estimation schemes and has gradually become the mainstream research direction in this field. This algorithm uses a combination of uniform motion (CV), uniform acceleration (CA), and uniform turning (CT) models. To improve the filtering accuracy for nonlinear systems, the Unscented Kalman (UKF) filter is used. It is a suboptimal filtering algorithm obtained by minimizing the posterior probability density. Its core is the UT transform, an effective method for calculating the statistical properties of random variables in nonlinear transformations.

[0049] Simulation results are as follows Figures 2a-2cAs shown, from top to bottom, the simulation results for dual-radar three-target tracking with systematic and random errors are presented, along with the single-radar multi-target tracking performance based on radar 1 measurements and the dual-radar multi-target tracking performance based on this invention. The filtering errors for the three targets calculated for both methods are shown in the table below:

[0050]

[0051] Among them, the target 1 filtering error refers to the average error in the x, y, and z directions of target 1, and the filtering error RMS is similar.

[0052] The table above shows that the average filtering error (average of three targets) of dual radar is reduced by 19.04% and the standard deviation of the average filtering error is reduced by 15.64% compared with single radar.

[0053] In summary, the systematic error of a dual-radar system will cause a slight deviation in the measurement values ​​of the two radars for the same target in a unified coordinate system. This deviation will produce incorrect correlation in the case of multiple targets at close range (such as flight formations). By correcting this deviation, this invention can make the correlation between point traces and flight paths in multi-target tracking problems more accurate, thus achieving better tracking results.

Claims

1. A real-time multi-target tracking method using dual radars that considers system error correction, characterized in that, Includes the following steps: Step 1: Set the radar system parameters, including sensor ID, sensor data transmission cycle, sensor latitude and longitude, measurement error, and detection range; After the radar transmits the point traces, the distance, azimuth, and elevation measurements of the two radars A and B are transformed into a unified Cartesian coordinate system, and the radar measurement errors are also transformed into Cartesian coordinates to form an observation dataset in the Cartesian coordinate system. Among them, the measurement values ​​and measurement errors in the Cartesian coordinate system are used for joint probability distribution data association, and the measurement values ​​and measurement errors in the radar spherical coordinate system are used for filtering and updating. Step 2: Use radar A's observations to initiate tracks for multiple targets. Use a logical method to initiate and terminate tracks. Assume that the sequence of observations contains N scan cycles. If the number of successful detections reaches the threshold M within a time window containing N scan cycles, then the track is successfully started. After the start is completed, continue to associate with the filtering error to maintain stability. Step 3: After a correct and stable multi-target track has been formed, add the observation data from radar B. The first set of measurement data from radar B encountered subsequently is shifted to coincide with the center of the graphic formed by the extension points of all tracks. A correction window w is set, and the shift S of the nth set of measurement data from radar B encountered subsequently is: x n This represents the offset of the nth set of measurement data from radar B. The measurement data of radar B is shifted according to the shift amount S, and the shifted measurement data is used as new measurement data in subsequent correlation and filtering. Step 4: Based on whether all measurement data fall into the tracking gate of each track extension point, a confirmation matrix is ​​formed. The confirmation matrix is ​​then split into multiple feasible events using a depth search algorithm. The maximum likelihood probability of each feasible event is calculated using the posterior probability formula. The probabilities of each feasible event are combined to form a joint correlation probability. Step 5: For each measurement data associated with each track, perform IMM-UKF filtering based on the joint association probability. The specific method is as follows: The input conditions of each unscented Kalman filter are a mixture of the estimates from the filters at the previous time step; For each unscented Kalman filter, given the re-initialized state and covariance matrix, filtering is performed after obtaining new measurements; Calculate the model probability for each filter; Calculate the overall estimate and overall estimate error covariance at the current time based on the state estimate and model probability of each filter; The state estimate and covariance estimate of each IMM-UKF filter are combined to obtain the final filtering result of the track.

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